The radius of a cylinder is increasing at a constant rate of 2 inches per minute. The volume remains a constant 440 cubic inches. At the instant when the radius of the cylinder is 44 inches, what is the rate of change of the height? The volume of a cylinder can be found with the equation V= Round your answer to three decimal places.

The rate of change of the height is approximately .

Step-by-step explanation:

From Geometry we know that volume of cylinder (), measured in cubic inches, is expressed by:

(1)

Where:

- Radius, measured in inches.

- Height, measured in inches.

Given that volume remains constant, the expression for the rate of change of the height (), measured in inches per minute, is:

(2)

Where is the rate of change of the radius, measured in inches per minute.

If we know that , and , then the rate of change of the height is:

The rate of change of the height is approximately .

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step-by-step explanation: